Three point charges of magnitude $5 \mu C , 0.16 \mu C$ and $0.3 \mu C$ are located at the vertices $A , B , C$ of a right angled triangle whose sides are $AB =3\,cm$, $BC =3 \sqrt{2}\,cm$ and $CA =3\,cm$ and point $A$ is the right angle corner. Charge at point $A$ experiences

$N$ of electrostatic force due to the other two charges.

Two electrons each are fixed at a distance $'2d'$. A third charge proton placed at the midpoint is displaced slightly by a distance $x ( x << d )$ perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency : $( m =$ mass of charged particle)

Total charge $-\,Q$ is uniformly spread along length of a ring of radius $R$. A small test charge $+q$ of mass m is kept at the centre of the ring and is given a gentle push along the axis of the ring.

$(a) $ Show that the particle executes a simple harmonic oscillation.

$(b)$ Obtain its time period.

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of:

Two fixed charges $4\,Q$ (positive) and $Q$ (negative) are located at $A$ and $B$, the distance $AB$ being $3$ $m$.

Write some important points for vector form of Coulomb’s law.